Stable periodic orbits in a pair of chaotic oscillators coupled by an extremely weak diffusive connection

Abstract

The present paper numerically and experimentally demonstrates that an extremely weak diffusive connection can induce a stable periodic orbit in coupled chaotic oscillators, where each individual oscillator has an unstable periodic orbit which dominates its chaotic attractor. The connection-induced stable periodic orbit is quite close to the unstable periodic orbit. The mechanism of this phenomenon is clarified on the basis of bifurcation analysis: When the coupling strength is varied from zero to an extremely small positive value, the unstable periodic orbit embedded within each individual chaotic attractor becomes stable via a period-doubling bifurcation and then disappears via a saddle-node bifurcation. These results are numerically observed in well-known chaotic oscillators, such as Rossler oscillators and logistic maps. Furthermore, an experimental verification of this phenomenon in coupled chaotic electronic circuits is presented.